Question

A ladder is kept at a distance of 15 cm from the wall such that the top of the ladder is at the height of 8 cm from the bottom of the wall. Find the length of the wall.​

Answer 1

Given:

Distance of the ladder from the wall (a) = 15 cm

Height of the ladder's top from the bottom of the wall (b) = 8 cm

We have a right-angled triangle where the ladder is the hypotenuse, and the wall and the ground form the other two sides.

According to the Pythagorean theorem:

c² = a² + b²

Substitute the given values:

c² = 15² + 8²

c² = 225 + 64

c² = 289

Take the square root of both sides to find the length of the wall (c):

c = √289

c = 17 cm

Therefore, the length of the wall is 17 centimeters.

Answer 2

The length of the wall is 17 cm.

Explanation:

Given:

• The ladder is kept at a distance of 15 cm from the wall.
• The top of the ladder is at the height of 8 cm from the bottom of the wall.

To find:

The length of the wall.

Solution:

Let the length of the ladder be x cm.

We can draw a diagram to represent the situation.

Attachment:

In the diagram, AB is the ladder, BC is the wall, and AC is the distance between the ladder and the wall.

We can apply the Pythagoras theorem to calculate the length of the ladder.

Pythagorean theorem:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the length of the ladder, which is x cm. The other two sides are BC = 8 cm and AC = 15 cm.

`\sf x^2= 8^2 + 15^2`

`\sf x^2 = 64 + 225`

`\sf x^2= 289`

`\sf x = √(289)`

`\sf x = 17`

Therefore, the length of the ladder is 17 cm.

Note: We must need the find the length of ladder not of wall.

Let Suppose, the ladder length is equal to length of wall.

Since the ladder is 17 cm long, the length of the wall is also 17 cm.